Abstract
In this paper we propose a method based on the algebraic Bethe ansatz leading to explicit results for the form factors of quantum spin chains in the thermodynamic limit. Starting from the determinant representations we retrieve in particular the formula for the two-spinon form factors for the isotropic XXX Heisenberg chain obtained initially in the framework of the q-vertex operator approach.
Highlights
The computation of form factors for integrable quantum field theories [1] and lattice models [2, 3] has always been one of the most important and challenging problems of the theory of quantum integrable systems. It gained even more importance since extremely good predictions for neutron scattering experiments were produced by the numerical analysis of the dynamical structure factors based on explicit analytic results for the form factors obtained from the Algebraic Bethe ansatz [4,5,6] or q-vertex operator approach [7, 8]
It was shown that the form factor approach is an excellent tool to compute the correlation function at finite temperature [12]
There are two main methods leading to the explicit evaluation of the form factors for the spin chains: multiple integral representation from the q-vertex operator approach obtained by M
Summary
The computation of form factors for integrable quantum field theories [1] and lattice models [2, 3] has always been one of the most important and challenging problems of the theory of quantum integrable systems. It is important to mention that all the results concerning the excited states of the massless spin chains in the Bethe ansatz framework in the zero-field case are based on the assumption that the tails of distribution of Bethe roots do not contribute to the leading order of measurable quantities in the thermodynamic limit. This assumption is already implicitly used in [30, 31] and its particular case, the condensation property of Bethe roots [32, 33] was very recently proved [34]. Some technical and computational difficulties are addressed in the appendices A and B
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